Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  e20 Structured version   Unicode version

Theorem e20 31763
Description: A virtual deduction elimination rule (see syl6mpi 62). (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
e20.1  |-  (. ph ,. ps  ->.  ch ).
e20.2  |-  th
e20.3  |-  ( ch 
->  ( th  ->  ta ) )
Assertion
Ref Expression
e20  |-  (. ph ,. ps  ->.  ta ).

Proof of Theorem e20
StepHypRef Expression
1 e20.1 . 2  |-  (. ph ,. ps  ->.  ch ).
2 e20.2 . . 3  |-  th
32vd02 31623 . 2  |-  (. ph ,. ps  ->.  th ).
4 e20.3 . 2  |-  ( ch 
->  ( th  ->  ta ) )
51, 3, 4e22 31696 1  |-  (. ph ,. ps  ->.  ta ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   (.wvd2 31593
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371  df-vd2 31594
This theorem is referenced by:  e20an  31764  tratrbVD  31900  onfrALTlem3VD  31926
  Copyright terms: Public domain W3C validator